If I designate an item before Shabbos for an acceptable purpose, it can become not muktza for me. Can another person, who I did not have in mind when I made my initial declaration the use that item?

My specific case is that snow fell on Friday and I designated that I would be using the fallen snow to make snow cones (snow+grape soda!) on Saturday. No additional snow fell between designation and consumption. Some were hesitant to try one due to muktza concerns.

I think the question is great, however the example of snow may specifically not be a good example as per the answer in the link that snow might always be Muktza per Rabbi Moshe Feinstein Zatzal.
–
Gershon GoldFeb 19 '14 at 18:24

@GershonGold Even something with no use can become not muktza if you explicitly designate it - even rocks.
–
yEzFeb 19 '14 at 18:47